$A$ uniform magnetic field exists in the region given by $\vec{B} = 3\hat{i} + 4\hat{j} + 5\hat{k} \, T$. $A$ rod of length $L = 5 \, m$ placed along the $y$-axis is moved along the $x$-axis with a constant speed $v = 1 \, ms^{-1}$. The induced e.m.f. in the rod is ......... $V$.

$A$ coil of cross-sectional area $A$ having $n$ turns is placed in a uniform magnetic field $B.$ When it is rotated with an angular velocity $\omega,$ the maximum $e.m.f.$ induced in the coil will be

Refer to the figure. The arm $PQ$ of the rectangular conductor is moved from $x=0$ outwards. The uniform magnetic field is perpendicular to the plane and extends from $x=0$ to $x=b$ and is zero for $x>b$. Only the arm $PQ$ possesses substantial resistance $r$. Consider the situation when the arm $PQ$ is pulled outwards from $x=0$ to $x=2b$ and is then moved back to $x=0$ with constant speed $v$. Obtain expressions for the flux,the induced emf,the force necessary to pull the arm,and the power dissipated as Joule heat. Sketch the variation of these quantities with distance.

$A$ conducting circular loop is placed in a uniform magnetic field,$B = 0.025 \, T$,with its plane perpendicular to the field. The radius of the loop is made to shrink at a constant rate of $1 \, mm \, s^{-1}$. The induced $emf$ when the radius is $2 \, cm$ is:

To measure a magnetic field between the magnetic poles of a loudspeaker, a small coil having $30$ turns and $2.5 \, cm^2$ area is placed perpendicular to the field and removed immediately. If the total charge flown through the coil is $7.5 \times 10^{-3} \, C$ and the total resistance of the wire and galvanometer is $0.3 \, \Omega$, then the magnitude of the magnetic field is

$A$ square loop of side $15 \ cm$ is being moved towards the right at a constant speed of $2 \ cm/s$ as shown in the figure. The front edge enters the $50 \ cm$ wide magnetic field region at $t=0$. The value of the induced emf in the loop at $t=10 \ s$ will be: